The quantity of energy E, which the atom gives up when the electron passes from an outer to an inner orbit, or which, conversely, is taken in when the electron passes from an inner to an outer orbit, may, as has been indicated, be regarded as the difference between the energy contents of the atom in the two stationary states. This difference may be expressed in the following way. Let us imagine that we eject the electron from a given orbit (_e.g._ No. 2 in the diagram) so that it is sent to “infinity,” or, in other words, is sent so far away from the nucleus that the attraction of the latter becomes negligible. To bring about this removal of the electron from the atom demands a certain amount of energy, which we can call the _ionizing work_ corresponding to the stationary orbit in question. We may here designate it as A₂. To eject the electron from the orbit No. 4 will demand a smaller amount of ionizing work, A₄. The difference A₂ - A₄ is accordingly the work which must be done to transfer the electron from the orbit No. 2 to the orbit No. 4. This is, however, exactly equal to the quantity E of energy which will be emitted as light when the electron passes from orbit No. 4 to orbit No. 2. If we call the frequency of this light ν, then from the relations E = _h_ν and E = A₂ - A₄, we have _h_ν = A₂ - A₄ If, now, in place of this specific example using the stationary orbits 2 and 4 we take any two orbits designated by the numbers _n″_ (for the inner) and _n′_ (for the outer), we can write for the frequency of the radiation emitted for a transition between these arbitrary states _h_ν = Aₙ˶ - Aₙˊ or Aₙ˶ Aₙˊ ν = ----- - ----- _h_ _h_ We have now reached the point where we ought to bring in the Balmer-Ritz formula for the distribution of the lines in the hydrogen spectrum. This formula may be written (see p. 59) K K _ν_ = ------ - ----- _n″_² _n′_² We can now see very clearly the similarity between the formula derived from the spectrum investigations and that derived from the two Bohr postulates. In both formulæ the frequency appears as the difference between two terms which are characterized in both cases by two integral numbers, in the first formula, numbers denoting two stationary orbits in the Bohr model for hydrogen, and in the second the two numbers which in the Balmer-Ritz formula for the hydrogen spectrum characterize, respectively, a series and one of the lines of the series. To obtain complete agreement we have merely to equate the corresponding terms in the two formulæ. Thus we have for any arbitrary integer _n_ Aₙ K ----- = ---- or _h_ _n_² _h_K Aₙ = ------ _n_²